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CppAD: A Package for Differentiation of C++ Algorithms

We refer to the
step by step conversion from an algorithm that computes function values
to an algorithm that computes derivative values
as Algorithmic Differentiation
(often referred to as Automatic Differentiation.)
Given a C++ algorithm that computes function values,
CppAD generates an algorithm that computes its derivative values.
A brief introduction to Algorithmic Differentiation can be found in
​wikipedia.
The CppAD documentation also contains an
​introduction
to AD as well as the mathematical
​theory
for CppAD's calculations.
The web site
​autodiff.org
is dedicated to research about, and promoting the use, of AD.